In this worksheet, we will practice adding, subtracting, multiplying, or dividing two given functions to create a new function and identifying the domain of the new function.

**Q1: **

What is the domain of the quotient , in terms of the domains of and ? Assume that both domains are subsets of the set of real numbers.

- A the union of the domain of and the domain of
- B the intersection of the domain of and the domain of
- C the larger of the domain of and the domain of
- D the intersection of the domain of and the domain of
- Ethe difference between the domain of and the domain of

**Q4: **

Find the domain of the function .

- A
- B
- C
- D

**Q5: **

If and , then find and fully simplify an expression for .

- A
- B
- C
- D

**Q6: **

If where , and where , find the value of if possible.

- A16
- B46
- C36
- Dundefined

**Q7: **

Given that , where , and , where , evaluate .

- A
- B724
- C
- D

**Q8: **

If and are two real functions where and , determine the value of if possible.

- A
- B
- C1
- Dundefined

**Q9: **

Given that , , and , determine in its simplest form.

- A
- B
- C
- D
- E

**Q10: **

Given that , , and , simplify the function , and determine its domain.

- A , domain
- B , domain
- C , domain
- D , domain
- E , domain

**Q11: **

Given that and find and state its domain.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q12: **

Given that and find the value of if possible.

- A
- B
- C0
- Dnot defined

**Q13: **

Given that and find and state its domain.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q14: **

If and are two real functions where and determine the domain of the function .

- A
- B
- C
- D

**Q15: **

If and are two real functions where and , find the domain of the function .

- A
- B
- C
- D
- E

**Q16: **

If where , and where , find and the domain of .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q17: **

If where , and where , then find and its domain.

- A ,
- B ,
- C ,
- D ,

**Q18: **

If where , and where , find and fully simplify and determine the domain of .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q19: **

If where , and where , find and the domain of .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q20: **

If and are two real functions where and , determine the domain of the function .

- A
- B
- C
- D
- E

**Q21: **

Given that and find and state its domain.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q22: **

Given that and find and state its domain.

- A ,
- B ,
- C ,
- D ,

**Q23: **

If and are two real functions where and , find the domain of the function .

- A
- B
- C
- D
- E

**Q24: **

Given that and are two real functions where and , find the value of if possible.

- A0
- B
- C35
- Dundefined

**Q25: **

Given that and are two real functions where and , find the value of if possible.

- A
- Bundefined
- C3
- D
- E